# Principal vertex operator representations for toroidal Lie algebras

@article{Billig1998PrincipalVO, title={Principal vertex operator representations for toroidal Lie algebras}, author={Yuly Billig}, journal={Journal of Mathematical Physics}, year={1998}, volume={39}, pages={3844-3864} }

We introduce the principal vertex operator representations for the toroidal Lie algebras generalizing the construction for the affine Kac–Moody algebras. We also represent the derivations of the toroidal algebras and introduce analogs of the Sugawara operators.

#### 57 Citations

Vertex operator algebras and the representation theory of toroidal algebras

- Mathematics
- 2001

An explicit vertex operator algebra construction is given of a class of irreducible modules for toroidal Lie algebras.

Irreducible Representations for Toroidal Lie Algebras

- Mathematics
- 1999

Abstract In this work a large number of irreducible representations with finite dimensional weight spaces are constructed for some toroidal Lie algebras. To accomplish this we develop a general… Expand

Integrable representations for generalized Virasoro-toroidal Lie algebras

- Mathematics
- 2003

Abstract In this paper, we give the structure of irreducible integrable modules of generalized Virasoro-toroidal Lie algebras, with finite-dimensional weight spaces and non-zero central charge.

Homogeneous Construction of the Toroidal Lie Algebra of Type A1

- Mathematics
- 2007

In this paper, we consider an analogue of the level two homogeneous construction of the affine Kac–Moody algebra by vertex operators. We construct modules for the toroidal Lie algebra and the… Expand

Vertex Operator Construction for the Toroidal Lie Algebra of Type F 4

- Mathematics
- 2003

Abstract The purpose of this work is to construct completely reducible vertex representations for the toroidal Lie algebra of type F 4.

Representations of the Twisted Heisenberg–Virasoro Algebra and the Full Toroidal Lie Algebras

- Mathematics
- 2007

An explicit construction of indecomposable modules for the twisted Heisenberg–Virasoro algebra and representations for the full toroidal Lie algebras are given.

IRREDUCIBLE REPRESENTATIONS FOR THE AFFINE-VIRASORO LIE ALGEBRA OF TYPE Bl

- Mathematics
- 2004

An explicit construction of irreducible representations for the affine-Virasoro Lie algebra of type Bl, through the use of vertex operators and certain oscillator representations of the Virasoro… Expand

Vertex representations for toroidal Lie algebra of type

- Mathematics
- 2005

The purpose of this work is to construct a class of homogeneous vertex representations for the extended toroidal Lie algebra of type G2, which are showed to be completely reducible.

Integrable representations for the twisted full toroidal Lie algebras

- Mathematics
- 2007

The purpose of this work is to classify irreducible integrable modules of the twisted full toroidal Lie algebra τ, with finite-dimensional weight spaces and non-zero central charges. There are three… Expand

Integrable Representations for Twisted Generalized Virasoro-Toroidal Lie Algebras

- Mathematics
- 2008

In this paper, we classify irreducible integrable modules of twisted generalized Virasoro-toroidal Lie algebras τ with finite-dimensional weight spaces.

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